(also known as Condorcet's method)
In a round robin tournament each competitor faces off against each other competitor. In a Virtual Round Robin election each candidate "A" has a match score against each other candidate "B" which is the number of ballots where someone voted A higher than B vs the number of ballots where someone voted B higher than A. If more people rank A higher than B than the other way round, A is said to have beaten B. Usually one choice emerges as undefeated and is elected the winner. If there is a tie where A beats B which beats C which beats A, then the tie is broken where the counts are closest. If A beats B 55:45, B beats C 54:46 and C beats A 43:47; this last victory of C over A is removed and then A is unbeaten and chosen as the winner.
Each ballot is normalized so that all ballots have the same magnitude. The modified ballots are summed, and the choice with the lowest sumarry rating is disqualified. Each ballot is then normalized again as if the disqualified choice was not there, redistributing the vote across the choices in proportion to the original ballot. The new modified ballots are summed and the process is repeated until there are two choices remaining and one choice wins over the other.
When using ratings ballots (0..10 etc.) IRNR is capable of getting better results than VRR.